Answer:
D. tan(θ) = 3√7/7
Explanation:
csc(θ) is equal to the hypotenuse over the opposite side, so if csc(θ) = -4/3, we can represent the angle with the following triangle
So, we can calculate the missing side using the Pythagorean theorem as follows
[tex]\begin{gathered} x=\sqrt[]{4^2-3^2} \\ x=\sqrt[]{16-9} \\ x=\sqrt[]{7} \end{gathered}[/tex]
Now, the tangent of the angle is calculated as:
[tex]\begin{gathered} \tan (\theta)=\frac{Opposite\text{ side}}{Adjacent\text{ side}} \\ \tan (\theta)=\frac{3}{\sqrt[]{7}} \end{gathered}[/tex]
Then, the tangent is equal to:
[tex]\tan (\theta)=\frac{3}{\sqrt[]{7}}\cdot\frac{\sqrt[]{7}}{\sqrt[]{7}}=\frac{3\sqrt[]{7}}{7}[/tex]
Therefore, the answer is
D. tan(θ) = 3√7/7
